# MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE

### Nasour Bagheri, Babak Sadeghiyan, Majid Naderi

#### 2008

#### Abstract

Ring hash structure is a new hash structure which has been introduced by Joux to strengthen the current hash structures against multi-collision attacks. In this paper, we present a cryptanalysis on Ring hash structure. We show that finding multi-collisions, i.e. 2k-way collision, for a Ring hash structure is not much harder than finding such multi-collisions for ordinary MD hash structure. The complexity of our attack is approximately log (n) times harder than the complexity of attacks against MD structures. We employ these multi-collisions to find a D-way pre-image for this structure. We show the complexity of finding 2K-way multi-collision and 2k-way preimage are O((k+1)x(n / 2)x2n/2 ) and O(kx n / 2x2n/2+2x2n ) respectively. We also show that Ring structure should not be used to create a hash function of 2n-bit length, by concatenatingmthis structure to any other hash structure of n-bit output length. We show that the time complexity of finding a collision for this concatenated structure is O((k+1)x(n / 2)x 2n /2 )that is much smaller than Ω(2n ), which is expected for a generic-birthday attack.

#### References

- Biham, E., Chen, R, and Joux, A., etc, 2005. Collisions of SHA-0 and Reduced SHA-1, Advances in Cryptology-EUROCRYPT'05, pp.36-57, SpringerVerlag.
- Damgard, I., 1990. A design principle for hash functions, in Advances in Cryptology - Crypto'89 (G. Brassard, ed.), no. 435 in Lecture Notes in Computer Science, pp. 416-427, Springer-Verlag.
- FIPS, 180-1, 1995. Secure hash standard. FIPS publication.
- Gauravaram, P., Millan, W., Dawson, E. and Viswanathan, K., 2006. Constructing Secure Hash Functions by Enhancing Merkle-Damgard Construction., Information Security and Privacy, (Batten, L., Safavi-Naini, R., ed.) volume 4058 of Lecture Notes in Computer Science, pp. 407-420, Springer.
- Joux, A., 2004. Multi-collisions in Iterated Hash Functions. Application to Cascaded Constructions Advances in Cryptology-CRYPTO'04, pp. 306-316, Springer-Verlag.
- Lucks,S. , 2005. A failure-friendly design principle for hash functions. In Bimal Roy, editor, Advances in Cryptology-ASIACRYPT'05, volume 3788 of Lecture Notes in Computer Science, pp. 474-494, SpringerVerlag.
- Merkle, R., C., 1990. One-way hash functions and DES in Advances in Cryptology - Crypto'89 (G. Brassard, ed.), no. 435 in Lecture Notes in Computer Science, pp. 428-446, Springer-Verlag.
- Rivest, R., L., 1992. The MD4 Message - Digest Algorithm. Network MIT laboratory for Computer Science and RSA Data Security , Inc RFC 1320.
- Rivest, R., L., 1992. The MD5 message-digest algorithm, Request for Comments (RFC1320), Internet Activities Board, Internet Privacy Task Force.
- Speirs, W., R. and Molly, J., 2007. Making large Hash Functions from small compression function. available:http://eprint.iacr.org/2007/239.ps.
- Su, S., Yang, Y., Yang, B. and Zhang, S., 2006. The Design and Analysis of a Hash Ring-iterative Structure, available: http://eprint.iacr.org/2006/384.pdf
- Wang, X., Yin, Y., L., and Yu, H., 2005. Finding collisions in the full SHA-1, Advances in CryptologyCRYPTO'05, pp. 17-36, Springer-Verlag.
- Wang, X. and Yu, H., 2005. How to Break MD5 and Other Hash Functions, Advances in Cryptology - EUROCRYPT'05, pp. 19-35, Springer-Verlag.

#### Paper Citation

#### in Harvard Style

Bagheri N., Sadeghiyan B. and Naderi M. (2008). **MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)* ISBN 978-989-8111-59-3, pages 278-284. DOI: 10.5220/0001917102780284

#### in Bibtex Style

@conference{secrypt08,

author={Nasour Bagheri and Babak Sadeghiyan and Majid Naderi},

title={MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE},

booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)},

year={2008},

pages={278-284},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001917102780284},

isbn={978-989-8111-59-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)

TI - MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE

SN - 978-989-8111-59-3

AU - Bagheri N.

AU - Sadeghiyan B.

AU - Naderi M.

PY - 2008

SP - 278

EP - 284

DO - 10.5220/0001917102780284